CAIE A-Level Mathematics 1.3.3 Circle Equations

Practise reading a circle's centre and radius, completing squares in expanded equations and forming circle equations from centres, points, diameters or geometric constraints.

Exam points

read the centre (a, b) and radius r directly from (x − a)² + (y − b)² = r²
complete squares in x² + y² + 2gx + 2fy + c = 0 to recover centre and radius
use a point, diameter endpoints or centre distance to determine the required radius squared

[Maximum number: 2]

Points A(-2,3), B(3,0) and C(6,5) lie on the circumference of a circle with centre D.

Find an equation of the circle.

$\left(x-\text { their } \mathrm{x}_{\mathrm{c}}\right)^{2}+\left(y-\text { their } y_{c}\right)^{2}\left[=r^{2}\right]$ or $\left(\text { their } x_{\mathrm{c}}-x\right)^{2}+\left(\text { their } y_{c}-y\right)^{2}=\left[r^{2}\right]$
M1
Use of circle equation with their centre
$(x-2)^{2}+(y-4)^{2}=17$
A1
Accept $x^{2}-4 x+y^{2}-8 y+3=0$ OE

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1.3.3—Circle equation question 1